43 citations · 87 across the 8 of their papers we have counts for
6 papers · 1 filter
The isodiametric problem with lattice-point constraints
M. A. Hernandez Cifre, A. Schuermann, F. Vallentin
In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is sh…
A generalization of Voronoi's reduction theory and its application
Mathieu Dutour Sikiric, Achill Schuermann, Frank Vallentin
We consider Voronoi's reduction theory of positive definite quadratic forms which is based on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed…
Three-dimensional antipodal and norm-equilateral sets
Achill Schuermann, Konrad Swanepoel
We characterize the three-dimensional spaces admitting at least six or at least seven equidistant points. In particular, we show the existence of norms on admitti…
On packing spheres into containers (about Kepler's finite sphere packing problem)
Achill Schuermann
In an Euclidean -space, the container problem asks to pack equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\…
Methods in the Local Theory of Packing and Covering Lattices
Achill Schuermann, Frank Vallentin
In this paper we are concerned with three lattice problems: the lattice packing problem, the lattice covering problem and the lattice packing-covering problem. One way to find opti…
Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8
Achill Schuermann, Frank Vallentin
We show that the Leech lattice gives a sphere covering which is locally least dense among lattice coverings. We show that a similar result is false for the root lattice E8. For thi…